{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Markov Random Fields\n",
    "## An image de-noising example: Ising Model\n",
    "\n",
    "A random markov field probabilistic model represented as a nondirected graph such that can be written as\n",
    "\n",
    "$$\n",
    "    p({\\bf x}) = \\frac{1}{Z} \\prod_c\\psi_c({\\bf x}_c)\n",
    "$$\n",
    "\n",
    "Where $Z = \\sum_{\\bf x}\\prod_c \\psi_c({\\bf x}_c)$, and the product runs over the *maximal* cliques in the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numba import jit\n",
    "from skimage.io import imread\n",
    "from numpy.random import seed, random\n",
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(576, 598)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "img = imread(\"img.jpeg\", as_gray=True)\n",
    "img_shape = img.shape\n",
    "img = np.round(img)\n",
    "img.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\{y_i\\}_i$ be the pixels of an observed noisy image. We suppose that the noisy image was generated using a noise-free image with pixels $\\{x_i\\}_i$ and randomly flippning the signs of the pixel with some small probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "final_noisy = np.copy(img)\n",
    "# p(flip) = 0.1\n",
    "mmap = random(size=(img_shape)) <= 0.2\n",
    "final_noisy[mmap] = np.abs(final_noisy[mmap] - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 227,
       "width": 460
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "ax[0].imshow(img, cmap=\"bone\")\n",
    "ax[1].imshow(final_noisy, cmap=\"bone\")\n",
    "ax[0].set_title(\"Original\", fontsize=15)\n",
    "ax[1].set_title(\"Corrupted\", fontsize=15)\n",
    "ax[0].axis(\"off\")\n",
    "ax[1].axis(\"off\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our energy function is given by\n",
    "$$\n",
    "    E({\\bf x}, {\\bf y}) = h\\sum_ix_i - \\beta \\sum_{\\{i,j\\}}x_ix_j - \\eta\\sum_ix_iy_i \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython=True)\n",
    "def find_neighbors(x, i, j):\n",
    "    \"\"\"\n",
    "    Find neighboring indices\n",
    "    \"\"\"\n",
    "    nx, ny = x.shape\n",
    "    rows, cols = [], []\n",
    "    if i > 0:\n",
    "        rows.append(i - 1)\n",
    "        cols.append(j)\n",
    "    if j > 0:\n",
    "        rows.append(i)\n",
    "        cols.append(j - 1)\n",
    "    if i < nx - 1:\n",
    "        rows.append(i + 1)\n",
    "        cols.append(j)\n",
    "    if j < ny - 1:\n",
    "        rows.append(i)\n",
    "        cols.append(j + 1)\n",
    "        \n",
    "    return rows, cols\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def E(x, y, h=0, beta=1.0, eta=2.1):\n",
    "    total_energy = h * x.sum() - eta * (x * y).sum()\n",
    "    total_energy = 0\n",
    "    nx, ny = x.shape\n",
    "    for i in range(nx):\n",
    "        for j in range(ny):\n",
    "            \n",
    "            rows, cols = find_neighbors(x, i, j)\n",
    "                \n",
    "            neighbor_energy = 0.\n",
    "            for row, col in zip(rows, cols):\n",
    "                neighbor_energy = neighbor_energy + x[row, col] * x[i, j]\n",
    "            \n",
    "            total_energy = total_energy - beta * neighbor_energy - eta * x[i, j] * y[i, j]\n",
    "            \n",
    "    return total_energy\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def neighbor_energy(x, i, j, beta):\n",
    "    \"\"\"\n",
    "    Sum of energies in the neighborhood\n",
    "    \"\"\"\n",
    "    rows, cols = find_neighbors(x, i, j)\n",
    "    energy = 0.\n",
    "    for row, col in zip(rows, cols):\n",
    "        energy = energy + x[row, col]\n",
    "    return x[i,j] * beta * energy\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def local_energy(x, y, i, j, h=0, beta=1.0, eta=2.1):\n",
    "    \"\"\"\n",
    "    Helper function to reach a field with lower energy. It\n",
    "    makes use of the fact that changing the sign of a node\n",
    "    affects only the cliques around it.\n",
    "    \"\"\"\n",
    "    rows, cols = find_neighbors(x, i, j)\n",
    "    neigh_energy = neighbor_energy(x, i, j, beta)\n",
    "    # Energy from neighbors in xy-clique\n",
    "    neigh_xy_energy = 0.0\n",
    "    for row, col in zip(rows, cols):\n",
    "        neigh_energy += neighbor_energy(x, row, col, beta)\n",
    "        neigh_xy_energy += eta * x[row, col] * y[row, col] \n",
    "    energy = h * x[i, j] - eta * x[i, j] * y[i, j] - neigh_energy - neigh_xy_energy\n",
    "    return energy\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def update_pixels(x, y):\n",
    "    nx, ny = x.shape\n",
    "    x = x.copy()\n",
    "    for i in range(nx):\n",
    "        for j in range(ny):\n",
    "            x[i,j] = 1\n",
    "            energy_plus = local_energy(x, y, i, j)\n",
    "            \n",
    "            x[i,j] = -1\n",
    "            energy_minus = local_energy(x, y, i, j)\n",
    "                \n",
    "            # Go to the state with lower energy\n",
    "            if energy_plus <= energy_minus:\n",
    "                x[i,j] = 1\n",
    "            else:\n",
    "                x[i,j] = -1\n",
    "                \n",
    "    return x\n",
    "\n",
    "\n",
    "@jit(nopython=True)\n",
    "def ising_learn(y):\n",
    "    x = y.copy()\n",
    "\n",
    "    E_hist = [E(x, y)]\n",
    "    while True:\n",
    "        x = update_pixels(x, y)\n",
    "        E_hist.append(E(x, y))\n",
    "        if E_hist[-1] / E_hist[-2] - 1 < 1e-6:\n",
    "            break\n",
    "    return E_hist, x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 35.6 s, sys: 208 ms, total: 35.8 s\n",
      "Wall time: 35.3 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "y = final_noisy.copy() * 2 - 1\n",
    "E_hist, x = ising_learn(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 244,
       "width": 460
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(8, 4))\n",
    "\n",
    "ax[0].imshow(y, cmap=\"bone\")\n",
    "ax[1].imshow(x, cmap=\"bone\")\n",
    "ax[0].set_title(f\"Corrupted\\n$E={E_hist[0]:,.2f}$\", fontsize=15)\n",
    "ax[1].set_title(f\"Restored\\n$E={E_hist[-1]:,.2f}$\", fontsize=15)\n",
    "ax[0].axis(\"off\")\n",
    "ax[1].axis(\"off\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'-1,790,474.20'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Optimal energy state\n",
    "format(E(img * 2 - 1, y), \",.2f\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 44210,   1097],\n",
       "       [  3227, 295914]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix((img * 2 - 1).ravel(), x.ravel())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Smaller Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.array([\n",
    "    [0, 1, 0, 0, 1],\n",
    "    [1, 0, 1, 0, 0],\n",
    "    [0, 1, 0, 1, 1]\n",
    "])\n",
    "\n",
    "y = 2 * y - 1\n",
    "\n",
    "def show_grid(x):\n",
    "    plt.pcolor(x[::-1], cmap=\"bone_r\", linewidths=3, edgecolors=\"tab:gray\")\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 235,
       "width": 352
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_grid(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 235,
       "width": 352
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, x = ising_learn(y)\n",
    "show_grid(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.5000000000000013\n",
      "-30.500000000000007\n"
     ]
    }
   ],
   "source": [
    "print(E(y, y))\n",
    "print(E(x, y))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
